Algebraic approach to optimal clone selection applied in metagenomic projects

Due to the wide diversity of unknown organisms in the environment, 99% of them cannot be grown in traditional culture medium in laboratories. Therefore, metagenomics projects are proposed to study microbial communities present in the environment, from molecular techniques, especially the sequencing. Thereby, for the coming years it is expected an accumulation of sequences produced by these projects. Thus, the sequences produced by genomics and metagenomics projects present several challenges for the treatment, storing and analysis such as: the search for clones containing genes of interest. This work presents the OCI Metagenomics, which allows defines and manages dynamically the rules of clone selection in metagenomic libraries, thought an algebraic approach based on process algebra. Furthermore, a web interface was developed to allow researchers to easily create and execute their own rules to select clones in genomic sequence database. This software has been tested in metagenomic cosmid library and it was able to select clones containing genes of interest. Copyright 2010 ACM.

Unfolding physics from the algebraic classification of spinor fields

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under such classification. In particular, we pithily focus on the new aspects - as well as current concrete possibilities. They mainly arise when we deal with some non-standard spinor fields concerning, in particular, their applications in physics. © 2012 Elsevier B.V.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Reticulados modulares em espaços euclidianos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

A family of asymptotically good lattices having a lattice in each dimension

A new constructive family of asymptotically good lattices with respect to sphere packing density is presented. The family has a lattice in every dimension n >= 1. Each lattice is obtained from a conveniently chosen integral ideal in a subfield of the cyclotomic field Q(zeta(q)) where q is the smallest prime congruent to 1 modulo n.

Codificação de canais em sistemas de comunicação sem fio baseado em reticulados

Pós-graduação em Engenharia Elétrica - FEIS

Solitons in atomic condensates, with optical lattices and field-induced dipole moments

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Algebraic solution of an anisotropic nonquadratic potential

We show that an anisotropic nonquadratic potential, for which a path integral treatment has been recently discussed in the literature, possesses the SO(2, 1) ⊗SO(2, 1) ⊗SO(2, 1) dynamical symmetry, and construct its Green function algebraically. A particular case which generates new eigenvalues and eigenfunctions is also discussed. © 1990.

Algebraic solution of an anisotropic ring-shaped oscillator

Using an algebraic technique related to the SO (2, 1) group we construct the Green function for the potential ar2 + b(r sin θ)-2 + c(r cos θ)-2 + dr2 sin2θ + er2 cos2θ. The energy spectrum and the normalized wave functions are also obtained. © 1990.

Tópicos de teoria dos números algébricos e aplicações em reticulados e equações diofantinas

Pós-graduação em Matemática Universitária - IGCE